The procedure for a normal imaging process can be summarized as follows: After positioning a patient in an MR tomograph, coils are positioned relative to the patient. The creation of a survey radiograph makes it possible to plan the image geometry in a workstation that interacts with the MR tomograph, and the k-space data are imaged. After the image reconstruction on a reconstruction computer, the images are displayed on the workstation for viewing and diagnosis by the viewer. Based upon this procedure, the invention relates to the imaging of the k-space data.
“Balanced Steady-State Free Precession” MRI sequences (also termed b-FFE, TrueFISP, or FIESTA [15]) are used for fast imaging, in order to obtain a higher signal-to-noise ratio, such as in comparison to FLASH sequences. Moreover, the b-SSFP sequence is used in order to obtain a fast T1/T2 contrast which, for example, is important in imaging the articular disc in the temporomandibular joint [23]. In comparison, FLASH can generate only T1 or proton-weighted contrast.
The k-space is sampled by a radial k-space trajectory that is composed of a plurality of radial profiles, of which each pass through the midpoint of the k-space [16]. Radial trajectories are less subject to movement artifacts and are therefore frequently used in order to image dynamic physiological processes [3].
In addition, radial trajectories, in comparison to Cartesian trajectories, are more robust with regard to incomplete sampling viewed in the direction of rotation, which is used for time-resolved imaging to improve the temporal resolution.
A reconstruction with a shiftable temporal section is used in order to further increase the refresh rate of the image. In conventional radial trajectories with a uniform distribution of the radial profiles, the size of the temporal section used for reconstruction is dictated by the number of profiles per image and must be selected before imaging. In most cases, the optimum size of the temporal section for reconstruction is unknown beforehand. Changing the size of the temporal section requires a re-imaging of the object with an adapted radial trajectory.
It was demonstrated in [33] that, in fact, when the radial profiles are arranged using the golden angle of 111.24 . . . ° so that the sequential profiles are spaced with the angle increment of the golden angle, a nearly even distribution of the profiles can be achieved for any number n of sequential profiles. This golden angle is the optimum arrangement, if the number n of radial profiles which is to be used for reconstructing an image is not constant, or is fixed before imaging [2]. Consequently, the number n of profiles in the reconstruction section, and hence the degree of undersampling, can be subsequently adapted to different degrees of movement.
For the sake of completeness, it is noted that, in the present application, the full circle is assumed to be Pi instead of 2*Pi, since the central beam trajectory is used in most sequences in MRI.
If the full circle in the golden section is divided (tau=(1+sqrt (5))/2, the golden angle Psigolden=Pi/tau of 111.2461 . . . ° is obtained, along with the associated supplementary angle (“small golden angle”) Pi−Psigolden of 68.7538 . . . °.
Due to the incoherent artifacts, the golden angle is used inter alia in combination with compressed sensing [5], as well as in WO 2013/159044 A1.
The combination of the golden angle arrangement with balanced SSFP is subject to disadvantages, since the large radial angle increment of 111.246° is achieved by a continuously and abruptly changing gradient scheme. This gradient scheme, in turn, induces large, abruptly changing eddy currents in the conductive parts of the main magnet, and therefore produces continuously changing inhomogeneities in the main magnet field. The eddy current effects influence the equilibrium of the balanced SSFP sequence and thereby produce strong image artifacts [1].
Bieri et al. propose two techniques to compensate for these artifacts [16]:
1. The k-space profiles are re-sorted so that two k-space profiles with the same or similar angle are always measured sequentially. This eliminates eddy current effects, and the equilibrium of the SSFP sequence is retained, which is also termed “spoke-pairing.” However, the temporal resolution of the dynamic image is halved. A “spoke” is a synonym for a k-space profile; all k-space profiles together are the k-space trajectory.2. The eddy-current-induced signal is suppressed by a small dephasing gradient which is aligned perpendicular to the slice position. This modifies the amplitude of the rephasing gradient (“through slice equilibration”). In practice, and when the angle increments are very large, this technique yields only unsatisfactory results, since the eddy currents that can be compensated for are limited. Moreover, this solution works only for two-dimensional images.
Alternatively, FLASH sequences are used that have a worse SNR and show a different contrast.
It is, moreover, desirable to find a constant angle increment Psi that achieves satisfactory uniformity for each number of n profiles. Given an angle increment of Psiopt, the optimum distribution for an image with precisely n profiles is Psiuniform=180°/n, since all of the gaps between the adjacent profiles are accordingly equal in size.
A uniform angle increment Psiuniform=Pi/P offers the best uniform radial sampling trajectory for a given number P of radial profiles. If the number P of profiles is variable, it was revealed that the trajectory with the golden angle is an optimum radial distribution for a random number of profiles.
In order to compare sampling trajectories, the sampling efficiency is calculated. The quality of a non-optimum distribution is defined by the sampling efficiency. A high uniformity yields a high sampling efficiency. The sampling efficiency SE (Psi, P) for a given angle increment Psi and for P radial profiles corresponds to the relationship between the signal-to-noise ratio SNRuniform of uniform sampling and the signal-to-noise ratio SNRPsi of sampling with the angle increment Psi [17]. The signal-to-noise ratio SNR can be derived directly from the sampling density of the sampling scheme [3]. The sampling efficiency is defined as:
      S    ⁢                  ⁢          E      P      ψ        =                    S        ⁢                                  ⁢        N        ⁢                                  ⁢                  R          ψ                            S        ⁢                                  ⁢        N        ⁢                                  ⁢                  R          uniform                      =                                        π            2                    /          P                                      ∑                          i              =              0                                      P              -              1                                ⁢                                    (                              Δ                ⁢                                                                  ⁢                                  Φ                  i                                            )                        2                              wherein ΔΦi is the average azimuth distance of the profile “i” to its two neighbors. The sampling efficiency of the golden angle is greater than 0.9732 for each number of profiles P, termed “n” in the remainder of the text.
By means of the “pseudo golden-ratio spiral imaging” method, it is possible to generate real-time MRT images of a talking person with favorable image quality and simultaneously acceptable sound quality [37].
From WO 2008/132659 A2, a device and a method are known for generating MRT images of a patient, wherein the k-space trajectories follow a so-called “Periodically Rotated Overlapping Parallel Lines with Enhanced Reconstruction” approach [38].